Question: Simplify the following expression: $p = \dfrac{r^2 + 13r + 40}{r + 8} $
Explanation: First factor the polynomial in the numerator. $ r^2 + 13r + 40 = (r + 8)(r + 5) $ So we can rewrite the expression as: $p = \dfrac{(r + 8)(r + 5)}{r + 8} $ We can divide the numerator and denominator by $(r + 8)$ on condition that $r \neq -8$ Therefore $p = r + 5; r \neq -8$